If you're still looking for games I can rec you some that haven't been mentioned yet.
Hokalovi is an equine sim game I stumbled upon just a few days ago that already has me hooked. The game orginally started in Hungary but now the game has an English translation (with a few errors but it's still playable). What got my attention was how pretty the artwork is for the horses (it's a traditional art style) and the fact there are both foal and adult artwork for each breed ranging from tiny Shetlands to Shires. It takes a little while to grasp the concept of the game but once you get it it's pretty simple (there's LOTS of clicking). The benefit to this game is its turn based (per each horse. How neat is that!), but it does not cap you on the number of turns you can have in a single real day so you could basically play all day and night if you wanted ha. The English side of the game is kinda dead so we're always looking for new players! It's a great way to pass time, the horses are cute and I really enjoy it.
Equiverse is another equine sim I was pretty active on until they started recoding it. There aren't as many horse breeds as other larger horse sim games but I found it pretty enjoyable. As any horse game there are plenty of options on how to play from just breeding horses for certain colors or to raise the best horse in your choice of disipline with the highest stats. Right now the game is going through a recode but don't let that stop you from registering; all horses and currency will be moved over to the new site once everything is done.
Exhibited is a virtual dinosaur breeding sim. It's just like any of the horse/dog breeding games but with dinosaurs. They also have a really fun battling system and the community is pretty nice.
Dynasty is a dog breeding game where a player can really go into depth with breeding dogs. You can choose to breed for height, a certain color, a certain coat length, and if you want to get funky you can even breed for certain qualities like a Doberman with curly fur or a Schnauzer that's the size of a Great Dane. The options really are endless with this game.
Equus Ipsum is another equine based sim. It's still in beta (last time I checked it was) so the community is pretty small and it's easy to get on the leader boards with your horses. The only downside to this game is there's no vacation mode and it's not turn based either so you've got to stay on top of logging in every day, feeding your horses, etc so that can become a hassle. The community is pretty fun on this one as well, easily the best community of any sim game I've been on.
And one last game I'd rec is Movement Sim. The game will be coming out soon but it looks amazing, I like their ideas for a horse sim, and I think it'll be worth something when it finally comes out. I usually check their facebook for updates on the game but here's the actual website.
I'm on all of those games (minus Equus Ipsum- I kinda quit because of the vacation mode thing ha) under this same username so if you wanna add me on any you can! Currently though I'm only active on Hokalovi (and here).
For more fics check out my main pseud!